27 citations · 56 across the 16 of their papers we have counts for
24 papers
Low-regularity finite element elasticity complexes with hybridizable stresses on tetrahedral Alfeld splits
Johnny Guzmán, Xuehai Huang
Finite element elasticity complexes of low regularity are constructed on tetrahedral Alfeld splits. In comparison with existing three-dimensional elasticity complexes on such split…
The Johnson-Krizek-Mercier elasticity element in any dimensions
Jay Gopalakrishnan, Johnny Guzman, Jeonghun J. Lee
Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components wi…
Low-order divergence-free approximations for the Stokes problem on Worsey-Farin and Powell-Sabin splits
Maurice Fabien, Johnny Guzman, Michael Neilan +1
We derive low-order, inf-sup stable and divergence-free finite element approximations for the Stokes problem using Worsey-Farin splits in three dimensions and Powell-Sabin splits i…
Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty
Erik Burman, Johnny Guzman
We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection--diffusion equation. For the time-discretisation we consider eit…
Estimation of the continuity constants for Bogovski\uı and regularized Poincaré integral operators
Johnny Guzman, Abner J. Salgado
We study the dependence of the continuity constants for the regularized Poincaré and Bogovski\uı integral operators acting on differential forms defined on a domain of $\mathbb…
Exact sequences on Worsey-Farin Splits
Johnny Guzman, Anna Lischke, Michael Neilan
We construct several smooth finite element spaces defined on three--dimensional Worsey--Farin splits. In particular, we construct , $H^1(\curl)$, and -conforming finite e…
Convergence of Lagrange finite elements for the Maxwell Eigenvalue Problem in 2D
Daniele Boffi, Johnny Guzman, Michael Neilan
We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange…
Obtaining higher-order Galerkin accuracy when the boundary is polygonally approximated
Todd Dupont, Johnny Guzman, Ridgway Scott
We study two techniques for correcting the geometrical error associated with domain approximation by a polygon. The first was introduced some time ago \cite{bramble1972projection}…
Stability and error analysis of a splitting method using Robin-Robin coupling applied to a fluid-structure interaction problem
Erik Burman, Rebecca Durst, Johnny Guzman
We analyze a splitting method for a canonical fluid structure interaction problem. The splittling method uses a Robin-Robin boundary condition, explicit strategy. We prove the meth…
Well-posedness and H(div)-conforming finite element approximation of a linearised model for inviscid incompressible flow
Gabriel Barrenechea, Erik Burman, Johnny Guzmàn
We consider a linearised model of incompressible inviscid flow. Using a regularisation based on the Hodge Laplacian we prove existence and uniqueness of weak solutions for smooth d…
New stability estimates for an unfitted finite element method for two-phase Stokes problem
Ernesto Cáceres, Johnny Guzmán, Maxim Olshanskii
The paper addresses stability and finite element analysis of the stationary two-phase Stokes problem with a piecewise constant viscosity coefficient experiencing a jump across the…
Exact smooth piecewise polynomial sequences on Alfeld splits
Guosheng Fu, Johnny Guzman, Michael Neilan
We develop exact piecewise polynomial sequences on Alfeld splits in any spatial dimension and any polynomial degree. An Alfeld split of a simplex is obtained by connecting the vert…
Cubic Lagrange elements satisfying exact incompressibility
Johnny Guzman, Ridgway Scott
We prove that an analog of the Scott-Vogelius finite elements are inf-sup stable on certain nondegenerate meshes for piecewise cubic velocity fields. We also characterize the diver…
Inf-sup stable finite elements on barycentric refinements producing divergence--free approximations in arbitrary dimensions
Johnny Guzman, Michael Neilan
We construct several stable finite element pairs for the Stokes problem on barycentric refinements in arbitrary dimensions. A key feature of the spaces is that the divergence maps…
Analysis of the finite element method for the Laplace--Beltrami equation on surfaces with regions of high curvature using graded meshes
Johnny Guzman, Alexandre Madureira, Marcus Sarkis +1
We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, , surface without boundary on gener…
The Scott-Vogelius finite elements revisited
Johnny Guzman, Ridgway Scott
We prove that the Scott-Vogelius finite elements are inf-sup stable on shape-regular meshes for piecewise quartic velocity fields and higher ().
Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems
Erik Burman, Johnny Guzman, Manuel A. Sanchez +1
We prove an optimal error estimate for the flux variable for a stabilized unfitted Nitsche finite element method applied to an elliptic interface problem with discontinuous constan…
Chip-firing on general invertible matrices
Johnny Guzman, Caroline Klivans
We propose a generalization of the graphical chip-firing model allowing for the redistribution dynamics to be governed by any invertible integer matrix while maintaining the long t…
A finite element method for high-contrast interface problems with error estimates independent of contrast
Johnny Guzman, Manuel A. Sanchez, Marcus Sarkis
We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove op…
Higher-order finite element methods for elliptic problems with interfaces
Johnny Guzman, Manuel A. Sanchez, Marcus Sarkis
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to th…
Discrete Extension Operators for Mixed finite element spaces on locally refined meshes
Mark Ainsworth, Johnny Guzmán, Francisco-Javier Sayas
The existence of uniformly bounded discrete extension operators is established for conforming Raviart-Thomas and Nédélec discretisations of and on locally refine…
Chip-firing and energy minimization on M-matrices
Johnny Guzmán, Caroline Klivans
We consider chip-firing dynamics defined by arbitrary M-matrices. M-matrices generalize graph Laplacians and were shown by Gabrielov to yield avalanche finite systems. Building on…
A Note on the Ladyzenskaja-Babuska-Brezzi Condition
Abner J. Salgado, Johnny Guzman, Francisco-Javier Sayas
The analysis of finite-element-like Galerkin discretization techniques for the stationary Stokes problem relies on the so-called LBB condition. In this work we discuss equivalent f…
Local energy estimates for the finite element method on sharply varying grids
Alan Demlow, Johnny Guzman, Alfred H. Schatz
Local energy error estimates for the finite element method for elliptic problems were originally proved in 1974 by Nitsche and Schatz. These estimates show that the local energy er…